Damascene Philosophy

ParadoxesX

The bootstrap paradox

A time traveller gives Shakespeare a copy of Hamlet, which Shakespeare copies and publishes. So who wrote Hamlet?

Reading time
4 min
Difficulty
Intermediate
Branch
Time
First posed
Robert Heinlein, 'By His Bootstraps', 1941; discussed by David Lewis, 1976
the book existsan older self takes it backa younger self copies it
An older self hands a younger self the book. The younger self publishes it. Who wrote it?

The puzzle

A literature student builds a time machine and travels back to 1599 to meet Shakespeare. She brings a copy of the Complete Works as a gift. Shakespeare, who has not yet written Hamlet, reads it, likes it, and copies it out in his own hand. Hamlet is published, becomes famous, and is reprinted for centuries, ending up in the student's Complete Works.

So who wrote Hamlet? Shakespeare copied it from the book. The book was printed from Shakespeare's version. The play exists, but it seems to have no author. The information came from nowhere. It is caught in a causal loop, a chain of causes that loops back on itself.

Unlike the grandfather paradox, there is no contradiction here. Everything is consistent: the student gives the book, Shakespeare copies it, it is published, the student acquires it. The puzzle is not that the story is impossible, but that it seems to leave something unexplained.

Why it matters

Causal loops are permitted, in principle, by certain solutions of general relativity, so the question of whether they are possible is not merely fictional.

The paradox also probes the principle of sufficient reason: the idea that everything has an explanation. A causal loop is a case where every event has a cause, but the loop as a whole has none.

Key terms

  • Causal loopA chain of events that causes itself, such as an object or piece of information carried back in time that becomes its own origin.
  • Closed timelike curveA path through spacetime that returns to its own past. Some solutions to Einstein's equations of general relativity allow them, which is why physicists take time travel puzzles seriously.
  • Principle of sufficient reasonThe principle, championed by Leibniz, that everything that is the case has a reason or explanation why it is so and not otherwise.
  • Self-consistency principleIgor Novikov's principle that any events involving time travel must be consistent with each other, so that a time traveller cannot change the past, only take part in it.

Proposed solutions

Proposed solution I

Loops are strange but possible

Causal loops are consistent. Each event in the loop is explained by an earlier one. Asking for an explanation of the whole loop is like asking why there is a universe.

Proposed solution II

Information cannot come from nowhere

A loop containing complex information is impossible, or at least so improbable that we should treat it as ruled out.

Proposed solution III

The loop corrects itself

Copying is never perfect. The loop is not perfectly closed; the version that comes back is slightly different, which breaks the paradox.

Each solution, tested

Loops are strange but possible

How it resolves the paradox
David Lewis argued that in a loop, every event has a cause, and so every event is explained. What is unexplained is the loop as a whole, and there is nothing incoherent about that: the history of the world as a whole may also lack an external explanation. Strange is not the same as impossible.
Why it doesn’t fully work
The information in the loop, all the words of Hamlet, comes from nowhere. That seems to violate a deep principle: complex, structured information requires a process that produces it.
What defenders say
Lewis accepted that such loops would be remarkable, but argued that remarkable is not impossible. Some suggest that loops would be overwhelmingly unlikely to contain complex information, which might explain why we never encounter them.

Information cannot come from nowhere

How it resolves the paradox
The physicist David Deutsch argues that knowledge can only arise through processes like evolution or creative thought. A loop in which Hamlet simply exists, without anyone ever composing it, violates this principle. Physically, loops might be possible only for simple objects whose states can be explained without creativity.
Why it doesn’t fully work
It is not clear that this is a law of physics rather than a principle about the kind of world we happen to inhabit.

The loop corrects itself

How it resolves the paradox
In a real loop, small changes might accumulate, so that the version Shakespeare copies is not exactly the version the student brought. Over many hypothetical iterations, the text would have been produced by a process of change. This turns the loop into something more like a spiral with a beginning.
Why it doesn’t fully work
This works only if we allow multiple iterations, which requires something like branching timelines. In a single, consistent timeline, there is only one loop.

Who argued what

  • Loops are strange but possible David Lewis
  • Information cannot come from nowhere David Deutsch
  • The loop corrects itself Various writers on time travel

Variations

By his bootstraps

In Robert Heinlein's 1941 story, a man is drawn through a time portal by an older version of himself, and over the course of the story becomes each of the characters who set events in motion. The title comes from the expression 'to pull oneself up by one's bootstraps', an impossible feat.

The watch

A time traveller gives her younger self a watch, which she keeps for decades and then carries back in time to give to her younger self. The watch was never manufactured. Unlike Hamlet, the watch would age over its looping journey, so it could not be the same watch at both ends unless something repaired it. Physical objects in loops raise extra problems.

Go deeper

Loops and the arrow of time

Entropy tends to increase over time. An object carried around a causal loop would have to return to exactly the state it started in, which seems to require entropy to decrease somewhere along the way. Some physicists argue that this, together with quantum effects, makes macroscopic causal loops vanishingly unlikely, even if the equations of general relativity allow them.

Related ideas

Paradox

The grandfather paradox

You travel back in time and prevent your grandparents from ever meeting. Then you are never born, so you never travel back. So they do meet. So you are born...

Question

Is time real?

Time feels like a river carrying us from past to future. Physics describes it more like a map, with no moving 'now' anywhere on it.

Question

Why is there something rather than nothing?

Nothing at all would have been simpler. No universe, no laws, no questions. Yet here everything is.

Thought experiment

Are you a Boltzmann brain?

Given enough time, random fluctuations could assemble a single brain with your memories out of chaos. In some cosmologies, such brains vastly outnumber real observers.

Further reading and sources

Open questions

  • Can something exist with no origin at all?
  • If a work of art had no author, would it still be a work of art?
  • Is a causal loop any stranger than a universe with no first cause?

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